Question: $\overline{BC} = 7$ $\overline{AC} = {?}$ $A$ $C$ $B$ $?$ $7$ $ \sin( \angle ABC ) = \frac{4\sqrt{65} }{65}, \cos( \angle ABC ) = \frac{7\sqrt{65} }{65}, \tan( \angle ABC ) = \dfrac{4}{7}$
Answer: $\overline{AC}$ is the opposite to $\angle ABC$ $\overline{BC}$ is adjacent to $\angle ABC$ SOH CAH TOA We know the adjacent side and need to solve for the opposite side so we can use the tan function (TOA) $ \tan( \angle ABC ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{\overline{AC}}{\overline{BC}}= \frac{\overline{AC}}{7} $ $ \overline{AC}=7 \cdot \tan( \angle ABC ) = 7 \cdot \dfrac{4}{7} = 4$